Question: Rewrite as a simplified fraction. ${3.1\overline{49} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3149.4949...\\ 10x &= 31.4949...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3118}$ ${x = \dfrac{3118}{990}} $ ${x = \dfrac{1559}{495}} \text{or} {3 \dfrac{74}{495}}$